(* Project Euler Problem 8
 * By Weisi Dai <weisi@x-research.com>
 *)

let ubound = 13

let bigNumber = """
73167176531330624919225119674426574742355349194934
96983520312774506326239578318016984801869478851843
85861560789112949495459501737958331952853208805511
12540698747158523863050715693290963295227443043557
66896648950445244523161731856403098711121722383113
62229893423380308135336276614282806444486645238749
30358907296290491560440772390713810515859307960866
70172427121883998797908792274921901699720888093776
65727333001053367881220235421809751254540594752243
52584907711670556013604839586446706324415722155397
53697817977846174064955149290862569321978468622482
83972241375657056057490261407972968652414535100474
82166370484403199890008895243450658541227588666881
16427171479924442928230863465674813919123162824586
17866458359124566529476545682848912883142607690042
24219022671055626321111109370544217506941658960408
07198403850962455444362981230987879927244284909188
84580156166097919133875499200524063689912560717606
05886116467109405077541002256983155200055935729725
71636269561882670428252483600823257530420752963450
"""

let bigNumberOneLine = (List.ofSeq (bigNumber.Replace("\n","")))

let numberAt i = 
    bigint ((int << string) bigNumberOneLine.[i])

let computeProduct fromIndex = 
    let rec computeProductFromTo (product: bigint) fromIndex toIndex =
        if fromIndex < toIndex then
            computeProductFromTo 
                (product * (numberAt fromIndex)) 
                (fromIndex + 1) 
                toIndex
        else
            (product * (numberAt fromIndex))
    computeProductFromTo (bigint 1) fromIndex (fromIndex + ubound - 1)
    

let rec dp fromIndex toIndex =
    if fromIndex = toIndex then
        computeProduct fromIndex
    else
        let mid = (fromIndex + toIndex) / 2
        Seq.max [dp fromIndex mid; 
                 dp (mid + 1) toIndex]

let problem8 = dp 0 (Seq.length(bigNumberOneLine) - ubound)
    
let main = printfn "The answer is %s." (string problem8)

main
